Gases and Pressure

Gases are one of the states of matter—but not just any state. They’re birthday-cake-fueled toddlers on a sugar high. They’re three-month-old puppies in a kibble factory. They’re bumper cars turned up to 11.

Oh. And they’re usually invisible.

Solids and liquids tend to stay in place once they’re in appropriate containers, but gases will expand to fill any available space. They move incredibly fast—like 1100 miles per hour fast—and are constantly bouncing off of each other and the walls of their container, putting pressure on everything around them. They will exploit even the tiniest holes and can collide up to a trillion times per second at normal pressures and temperatures.

All this energy can do a lot of good—under the right circumstances. Put those gas molecules under pressure, and they’ll hit the walls of the container so many times that they’ll exert pressure of their own. This can be used to drive pistons or steam engines (or lift the lid off your pasta pot). They can also undergo reactions with each other or the walls of the container.

But since the movement of gases seems so random, how do we predict what size container or how much pressure we’ll need?

The Ideal Gas Law

Unlike toddlers, gases have one secret weakness: although individual molecules move randomly, on average, gases actually behave in statistical ways that can be described by a few basic laws. These laws are pretty intuitive and match what most of our experience with gases (things like putting air in a balloon or boiling water in a pot). Once you know these rules, it’s possible to predict how many moles of gas you’ll need at a certain pressure and temperature to get your desired volume or how to change the temperature to get the necessary pressure.

The three main laws are:

Boyle’s law: to decrease pressure, you should increase volume (and vice versa). When the lid on your pasta pot starts to rattle as the water begins to boil, you know the pressure is building up. When you take the lid off, the steam suddenly has a lot more space available to it, so the pressure goes back down to normal. This is expressed as P = K/V, where P is pressure, K is a constant, and V is volume. They are inversely

Charles’s Law: If you want to increase the volume of a gas, raise the temperature. This makes sense – the more energy the gas molecules (or sugar-fueled toddlers) have, the faster they’ll move and the more space they’ll need. This is written as V = KT, where V is volume, K is a constant, and T is the temperature in Kelvins.

Avogadro’s Law: If you add more molecules or moles of gas to a flexible container like a balloon, the volume will increase. We write this as V = nK, where n is the number of moles of gas.

If you combine all three of these laws, you get the Ideal Gas Law: PV = nRT. That mysterious constant K that we kept seeing turns out to be something called the Rydberg constant, which is equal to 0.08206 liter-atmospheres per mole-Kelvins. It helps keep all of the rest of the variables properly proportioned.

The Kinetic Molecular Theory of Gases

All of those laws intuitively make sense from what we know of gases in the real world. But where does this behavior come from? The Kinetic Molecular Theory of Gases helps explains why some of these relationships are true, and it starts with these five assumptions:

Gases travel from one point to another in straight lines

Gases have no appreciable volume

Collisions between molecules are elastic (there is no loss of energy)

Gas molecules do not influence each other’s movement by attracting or repelling each other

The kinetic energy of each molecule depends on its temperature in Kelvin

In the real world or in extreme pressures or temperatures, a lot of these assumptions start to break down, but they are still useful assumptions in many cases.

The Big Picture

These laws help lay the groundwork for everything from how much work a gas can do (by exerting pressure on, say, a piston) to how quickly two different kinds of gases will react with each other (more collisions will generally produce more reactions). By getting a good grasp of the relationships between pressure, temperature, volume, and moles, you’ll have all the information you need to conquer gaseous reactions. Unfortunately, it probably won’t help you calm down a room full of wired toddlers—but it will help you pass the AP Chemistry test!